Python: Add existing NodeGroup to Material
You can do something like this: create the node group instance and set the existing node group as node tree for this new instance.
import bpy

C = bpy.context

def instantiate_group(nodes, data_block_name):
    group = nodes.new(type='ShaderNodeGroup')
    group.node_tree = bpy.data.node_groups[data_block_name]
    return group

instantiate_group(C.object.material_slots[0].material.node_tree.nodes, 'NodeGroup')